I have double checked the Read & write permissions. The folder is Lightroom Masters which is set by Lightroom!

Hello Speck.

You do have a permissions issue..... they just seem to pop up on Mac OS.

What are you meaning "folder isLightroom Masters is set by Lightroom"? Lightroom does not create a Masters folder by itself, are you meaning the permissions are set by Lightroom?? That is not correct either...

Let us call them another name as you are using an Aperture/Apple type name which will confuse.

With Lightroom there are no masters just the images where ever you have directed Lightroom or the OS to put them.....

So let us rename your Masters Folders..... maybe you can call them Images 1 and Images 2 for now. Change the name IN LIGHTROOM by ctrl+clicking on the bame in the Folder Panel and renaming there....

Now for the folder that you can't import into ... it is a Permissions issue and this is seen often, why it happens I am not sure but it does. Did you check the "Apply to Enclosed Items when setting the Permissions here:

Great news, however do you still have folders with the same name in different locations?? If yes I would either change the names so they are unique or consider merging them. Merging could be done in Lightroom slowly and carefully moving files one folder at a time...